3.44.58 \(\int (55+e^2 (44-22 x)-11 x-11 e^4 x) \, dx\)

Optimal. Leaf size=21 \[ \frac {11}{2} \left (1+2 x-\left (-4+x+e^2 x\right )^2\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.33, number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {6} \begin {gather*} -\frac {11}{2} \left (1+e^4\right ) x^2-11 e^2 (2-x)^2+55 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[55 + E^2*(44 - 22*x) - 11*x - 11*E^4*x,x]

[Out]

-11*E^2*(2 - x)^2 + 55*x - (11*(1 + E^4)*x^2)/2

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (55+e^2 (44-22 x)+\left (-11-11 e^4\right ) x\right ) \, dx\\ &=-11 e^2 (2-x)^2+55 x-\frac {11}{2} \left (1+e^4\right ) x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 36, normalized size = 1.71 \begin {gather*} -11 \left (-5 x-4 e^2 x+\frac {x^2}{2}+e^2 x^2+\frac {e^4 x^2}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[55 + E^2*(44 - 22*x) - 11*x - 11*E^4*x,x]

[Out]

-11*(-5*x - 4*E^2*x + x^2/2 + E^2*x^2 + (E^4*x^2)/2)

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fricas [A]  time = 0.52, size = 27, normalized size = 1.29 \begin {gather*} -\frac {11}{2} \, x^{2} e^{4} - \frac {11}{2} \, x^{2} - 11 \, {\left (x^{2} - 4 \, x\right )} e^{2} + 55 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-11*x*exp(1)^4+(-22*x+44)*exp(1)^2-11*x+55,x, algorithm="fricas")

[Out]

-11/2*x^2*e^4 - 11/2*x^2 - 11*(x^2 - 4*x)*e^2 + 55*x

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giac [A]  time = 0.12, size = 27, normalized size = 1.29 \begin {gather*} -\frac {11}{2} \, x^{2} e^{4} - \frac {11}{2} \, x^{2} - 11 \, {\left (x^{2} - 4 \, x\right )} e^{2} + 55 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-11*x*exp(1)^4+(-22*x+44)*exp(1)^2-11*x+55,x, algorithm="giac")

[Out]

-11/2*x^2*e^4 - 11/2*x^2 - 11*(x^2 - 4*x)*e^2 + 55*x

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maple [A]  time = 0.02, size = 26, normalized size = 1.24

method	result	size
gosper	\(-\frac {11 x \left (x \,{\mathrm e}^{4}+2 \,{\mathrm e}^{2} x -8 \,{\mathrm e}^{2}+x -10\right )}{2}\)	\(26\)
risch	\(-\frac {11 x^{2} {\mathrm e}^{4}}{2}-11 x^{2} {\mathrm e}^{2}+44 \,{\mathrm e}^{2} x -\frac {11 x^{2}}{2}+55 x\)	\(29\)
norman	\(\left (44 \,{\mathrm e}^{2}+55\right ) x +\left (-\frac {11 \,{\mathrm e}^{4}}{2}-11 \,{\mathrm e}^{2}-\frac {11}{2}\right ) x^{2}\)	\(30\)
default	\(-\frac {11 x^{2} {\mathrm e}^{4}}{2}+{\mathrm e}^{2} \left (-11 x^{2}+44 x \right )-\frac {11 x^{2}}{2}+55 x\)	\(33\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-11*x*exp(1)^4+(-22*x+44)*exp(1)^2-11*x+55,x,method=_RETURNVERBOSE)

[Out]

-11/2*x*(x*exp(1)^4+2*x*exp(1)^2-8*exp(1)^2+x-10)

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maxima [A]  time = 0.38, size = 27, normalized size = 1.29 \begin {gather*} -\frac {11}{2} \, x^{2} e^{4} - \frac {11}{2} \, x^{2} - 11 \, {\left (x^{2} - 4 \, x\right )} e^{2} + 55 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-11*x*exp(1)^4+(-22*x+44)*exp(1)^2-11*x+55,x, algorithm="maxima")

[Out]

-11/2*x^2*e^4 - 11/2*x^2 - 11*(x^2 - 4*x)*e^2 + 55*x

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mupad [B]  time = 0.06, size = 24, normalized size = 1.14 \begin {gather*} x\,\left (44\,{\mathrm {e}}^2+55\right )-x^2\,\left (11\,{\mathrm {e}}^2+\frac {11\,{\mathrm {e}}^4}{2}+\frac {11}{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(55 - 11*x*exp(4) - exp(2)*(22*x - 44) - 11*x,x)

[Out]

x*(44*exp(2) + 55) - x^2*(11*exp(2) + (11*exp(4))/2 + 11/2)

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sympy [A]  time = 0.06, size = 27, normalized size = 1.29 \begin {gather*} x^{2} \left (- \frac {11 e^{4}}{2} - 11 e^{2} - \frac {11}{2}\right ) + x \left (55 + 44 e^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-11*x*exp(1)**4+(-22*x+44)*exp(1)**2-11*x+55,x)

[Out]

x**2*(-11*exp(4)/2 - 11*exp(2) - 11/2) + x*(55 + 44*exp(2))

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